Divisibility of Magnitude in De Generatione et Corruptione I.2 GC I.2 is principally dedicated to the presentation and subsequent refutation of an argument alleging that magnitude is indivisible. Offered at 316a14-316b18, the argument has the form of a reductio ad absurdum and appears to prove that the divisibility thesis implies absurd consequences. The reductio is refuted later in the chapter (317a2-12), with the refutation becoming a vehicle for a proper characterization of what it is for magnitude to be divisible, or so I ague. ‘Magnitude’ here refers both to bodily and mathematical magnitude, by which it is meant lines, planes and geometrical solids. Since Philoponus, the reductio is thought to be an argument by Democritus and Aristotle’s aim in this chapter to refute the Democritean ontology.1 Commentators insist on attributing it to Democritus, even though they acknowledge that it relies heavily on Aristotelian doctrine.2 Skeptical voices have been raised, but they have been few and unconvincing,3 the chief reason being that they fail to present Aristotle with an alternative motivation for rehearsing and refuting the argument. Two aporiai form the backbone of the chapter. The first, at 315b20-3, warns of a threat to the divisibility thesis and outlines the aim of the chapter as being to remove it. The second, at 316b19-27, explains this threat. Correctly understood, the first aporia also lays it down that the atomist ontology is already refuted, with no prospect of being resurrected. It is unlikely to be the threat of which that aporia warns. Still a further refutation of atomism would not therefore serve the chapter’s aims. Moreover, the chapter’s use of the terms ‘σῶµα’ and ‘µέγεθος’ casts further doubt on the claim that the reductio is by Democritus. Fimally, the argument is all too obviously flawed to have been used by Democritus, or anyone for that matter, in support of atomism. To the extent that GC I.2 has been used as evidence for 1See Joachim (1922), 76; Williams (1982); Luria (1933), 129-133; 23 ff.; Schramm (1962), 245-264; Miller (1982), 87-111; Barnes (1982); 356 ff.; Makin (1993), 49-62; Furley (1967), 85-87. Also Sedley (2004): “Why this elaborately contrived refutation of Democritean atomism?” (p. 82). 2 Rosen & Malink (2012) correctly point out that the reductio is based on a view Aristotle says was “discovered by himself, as the result of substantial theoretical work on his part”. But neither can resist the temptation of attributing the argument to Democritus: the argument says Rosen & Malink “can be regarded as a combination of Democritean and Aristotelian elements” (p. 31). They do not explain what the Democritean element is, though one may assume they take it to be the argument’s apparent support for atomism. 3 Cherniss (1935), 113, remarks that the reductio is offered as a reasoning that makes people think there are atomic bodies. Mau (1954), 25-6, is also skeptical that it is by Democritus. Democritean doctrine and in particular the view that Democritus rejected mathematical divisibility,4 the results of this part of the paper will have a bearing on that question too. The reductio could be an argument by atomist sympathizers of Speusippean or Xenocratean persuasion and familiar with Aristotelian doctrine. It could even be by Aristotle himself. Be that as it may, I worry that focusing on it as Democritean completely misses the key issue with which Aristotle is here most anxious to grapple. As the second of the two aporiai mentioned above makes clear, this is to remove a threat to the grounds for the position of Physics III.6 that the infinite is an attribute of magnitude (206b5-9). Prima facie, the difficulty is a reductio argument alleging that the proposed grounding is incoherent, thereby threatening the divisibility thesis. But this is a ploy Aristotle uses in order to expose a view on point assumed by the reductio that conflicts with his conception of magnitude and sharply to dissociate it from his own, which he then articulates. On that basis, he is able coherently to ground the position of Physics III.6 that the infinite is an attribute of magnitude. I In the first chapter of the GC Aristotle outlines important goals for this work. Chief among them is to offer accounts of unqualified generation and corruption (περὶ γενέσεως καὶ φθορᾶς τῆς ἁπλῆς) doing justice to the intuition that they are radically different form each other and, no less importantly, each is likewise different from alteration (ἀλλοίωσιν). Properly being able to account for all three and for bringing out their differences, he considers an adequacy test for any physical theory (314b12-17).5 Generation and corruption are discussed in chapter I.3 and alteration in I.4, which naturally raises this question; why does the discussion of the items on the agenda broadcasted in the first chapter not begin here? What is the important issue with which must GC I.2 must deal before the announced program can be set under way? GC I.2 begins by recalling the extended criticisms GC I.1 levels against previous thinkers for failing to account properly for 4‘Mathematical divisibility’ refers to the view that what Aristotle calls intelligible magnitude or intelligible body, namely the lines, planes and solids studied by geometers are divisible. If Democritus denies that atoms considered as mathematical solids are divisible or that parts can be marked in an atom, he is likely to be committed to mathematical indivisibility. 5 So in GC I.1 Aristotle offers detailed criticisms of previous thinkers for failing to account for generation, corruption and alteration. Some, he says, claim that everything is really one (ἕν τι τὸ πᾶν), and consequently think of generation and corruption as being merely alteration; others, as for instance Anaxagoras (314a13-6) and Empedocles (314b6-8) fail to distinguish between generation, corruption and alteration even though they postulate the existence of more than one elements. 2 generation, corruption and alteration. But unlike GC I.1, it singles out one thinker for praise. Democritus is applauded for offering accounts of generation and corruption and appreciating the difference between them as wells as the difference of each from alteration. On Democritus’ account, as Aristotle reports it, generation happens by association (σύγκρισις) and corruption by dissociation (διάκρισις) (315b6-9). There is generation when atoms associate to form stable configurations and corruption when they dissociate, with the configurations they previously formed being destroyed. In alteration, we have merely a change of position of the atoms comprising a particular configuration they jointly form, one that does not, however, bring about the destruction of that configuration.6 Here we have, one might think, the motivation for postponing the account of generation and corruption to the next chapter. Democritus offers competing accounts of generation, corruption and alteration. If atomism is left standing, Aristotle’s forthcoming account will have a competitor. Consequently, one might think, this chapter is dedicated to refuting Democritean and Leucippean atomism7 in order for Aristotle’s account to get the spoils. But this interpretation faces an obstacle. Nowhere in this chapter does Aristotle signal that he needs to refute atomism to serve his purpose. On the contrary, he signals that he has refuted atomism already. He says early on and long before the reductio that the Democritean ontology defies reason (πολλὴν ἔχει ἀλογίαν; 315b33). Also, the first horn of the aporia at 315b20-3, states that if generation happens by association, impossible consequences follow. These impossible consequences are certain to include the atomist ontology. Generation as association is the account of the Atomists, and of no other as far as we know. In context, then, generation as association implies atomism, and so what Aristotle says here, if only by implication, is that he has already shown atomism to be impossible. And he unequivocally confirms that he is already done with proving that when he says a little later in the chapter, at 316b16-8, that he has proved in other works that atomism is impossible.8 GC I.2 presupposes, 6 Democritus would presumably account for natural growth (αὔξησις) and diminution (φθίσις) by means of a similar mechanism he accounts for generation and corruption. A configuration grows bigger when additional atoms join in, or smaller when some of the atoms forming it depart, while the configuration itself persists, becoming larger or smaller respectively. 7 With ‘atomism’ I refer to the views of Democritean and Leucippean and by ‘Atomists’ to Democritus and Leucippus. I assume there is no difference between the views of the two men. So, using the name of only one of them, when I do, is no indication that I’m referring to his view as opposed to those of the other. 8Οὐ µὴν ἀλλὰ καὶ ταῦτα θεµένοις οὐχ ἧττον συµβαίνει ἀδύνατα. Ἔσκεπται δὲ περὶ αὐτῶν ἐν ἑτέροις. See for instance Phys. VI and more importantly De Caelo 303a3 ff. One of the previous work referred to here could well be the De Caelo, of which the Generatione et Corruptione, is presumably the sequel. If so, there is still less of a reason to engage anew in a recently undertaken task. 3 and says in so many words in several passages, that atomism is both unworkable and already refuted, which makes it odd that it should be dedicated to yet another refutation. We will be better able to understand the issue to be addressed in this chapter, if we return to the aporia at 315b20-3. We recall the first horn broadcasting impossible consequences to follow if generation is association, and identified the ontology on which this account rests as such a consequence.